Data structure: \(O = (W, A, Z, Y)\)
Underlying data generating process, \(P_{U,X}\)
## W A Z Y
## Min. :-3.78451 Min. :0.0000 Min. :0.0000 Min. :0.0000
## 1st Qu.:-0.68155 1st Qu.:0.5865 1st Qu.:0.0000 1st Qu.:0.0000
## Median :-0.01227 Median :1.9861 Median :0.0000 Median :1.0000
## Mean :-0.01301 Mean :2.1076 Mean :0.4897 Mean :0.5903
## 3rd Qu.: 0.68180 3rd Qu.:3.3863 3rd Qu.:1.0000 3rd Qu.:1.0000
## Max. : 4.03302 Max. :5.0000 Max. :1.0000 Max. :1.0000
## Summary of A given W < -1:
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.000 1.275 2.611 2.644 4.110 5.000
## Summary of A given -1 < W <= 0:
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.0000 0.8855 2.2639 2.3088 3.6422 5.0000
## Summary of A given 0 < W <= 1:
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.0000 0.3753 1.7284 1.9188 3.1381 5.0000
## Summary of A given 1 < W:
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.000 0.000 1.155 1.519 2.536 5.000
## CV selected lambda (from one sample): 0.00669857527625325
## The average of CV selected lambdas (from 1000 sample): 0.00805053386604685 The average of CV selected lambdas (from 1000 sample): 0.00805577329430703 The average of CV selected lambdas (from 1000 sample): 0.00805745619998476
## z=1:
## z=0:
## Undersmoothed lambda: 0.0015646006085061
## which is 0.233572146909012 * lambda_CV
## The average of unsersmoothed lambda (from 1000 sample): 0.00198207951272976
## which is 0.250582242951133 * the average of 1000 lambda_CV The average of unsersmoothed lambda (from 1000 sample): 0.00198377327801413
## which is 0.250548433156365 * the average of 1000 lambda_CV
## z=1:
## z=0:
## TableGrob (7 x 4) "arrange": 7 grobs
## z cells name grob
## 1 1 (2-3,2-3) arrange gtable[layout]
## 2 2 (4-5,1-2) arrange gtable[layout]
## 3 3 (4-5,3-4) arrange gtable[layout]
## 4 4 (6-7,1-2) arrange gtable[layout]
## 5 5 (6-7,3-4) arrange gtable[layout]
## 6 6 (3-3,4-4) arrange gtable[guide-box]
## 7 7 (1-1,1-4) arrange text[GRID.text.5833]
## TableGrob (7 x 4) "arrange": 7 grobs
## z cells name grob
## 1 1 (2-3,2-3) arrange gtable[layout]
## 2 2 (4-5,1-2) arrange gtable[layout]
## 3 3 (4-5,3-4) arrange gtable[layout]
## 4 4 (6-7,1-2) arrange gtable[layout]
## 5 5 (6-7,3-4) arrange gtable[layout]
## 6 6 (3-3,4-4) arrange gtable[guide-box]
## 7 7 (1-1,1-4) arrange text[GRID.text.6152]
## TableGrob (7 x 4) "arrange": 7 grobs
## z cells name grob
## 1 1 (2-3,2-3) arrange gtable[layout]
## 2 2 (4-5,1-2) arrange gtable[layout]
## 3 3 (4-5,3-4) arrange gtable[layout]
## 4 4 (6-7,1-2) arrange gtable[layout]
## 5 5 (6-7,3-4) arrange gtable[layout]
## 6 6 (3-3,4-4) arrange gtable[guide-box]
## 7 7 (1-1,1-4) arrange text[GRID.text.6471]
## TableGrob (7 x 4) "arrange": 7 grobs
## z cells name grob
## 1 1 (2-3,2-3) arrange gtable[layout]
## 2 2 (4-5,1-2) arrange gtable[layout]
## 3 3 (4-5,3-4) arrange gtable[layout]
## 4 4 (6-7,1-2) arrange gtable[layout]
## 5 5 (6-7,3-4) arrange gtable[layout]
## 6 6 (3-3,4-4) arrange gtable[guide-box]
## 7 7 (1-1,1-4) arrange text[GRID.text.6790]
## TableGrob (7 x 4) "arrange": 7 grobs
## z cells name grob
## 1 1 (2-3,2-3) arrange gtable[layout]
## 2 2 (4-5,1-2) arrange gtable[layout]
## 3 3 (4-5,3-4) arrange gtable[layout]
## 4 4 (6-7,1-2) arrange gtable[layout]
## 5 5 (6-7,3-4) arrange gtable[layout]
## 6 6 (3-3,4-4) arrange gtable[guide-box]
## 7 7 (1-1,1-4) arrange text[GRID.text.7109]
## TableGrob (7 x 4) "arrange": 7 grobs
## z cells name grob
## 1 1 (2-3,2-3) arrange gtable[layout]
## 2 2 (4-5,1-2) arrange gtable[layout]
## 3 3 (4-5,3-4) arrange gtable[layout]
## 4 4 (6-7,1-2) arrange gtable[layout]
## 5 5 (6-7,3-4) arrange gtable[layout]
## 6 6 (3-3,4-4) arrange gtable[guide-box]
## 7 7 (1-1,1-4) arrange text[GRID.text.7428]
## TableGrob (7 x 4) "arrange": 7 grobs
## z cells name grob
## 1 1 (2-3,2-3) arrange gtable[layout]
## 2 2 (4-5,1-2) arrange gtable[layout]
## 3 3 (4-5,3-4) arrange gtable[layout]
## 4 4 (6-7,1-2) arrange gtable[layout]
## 5 5 (6-7,3-4) arrange gtable[layout]
## 6 6 (3-3,4-4) arrange gtable[guide-box]
## 7 7 (1-1,1-4) arrange text[GRID.text.7747]
## TableGrob (7 x 4) "arrange": 7 grobs
## z cells name grob
## 1 1 (2-3,2-3) arrange gtable[layout]
## 2 2 (4-5,1-2) arrange gtable[layout]
## 3 3 (4-5,3-4) arrange gtable[layout]
## 4 4 (6-7,1-2) arrange gtable[layout]
## 5 5 (6-7,3-4) arrange gtable[layout]
## 6 6 (3-3,4-4) arrange gtable[guide-box]
## 7 7 (1-1,1-4) arrange text[GRID.text.8066]
## TableGrob (7 x 4) "arrange": 7 grobs
## z cells name grob
## 1 1 (2-3,2-3) arrange gtable[layout]
## 2 2 (4-5,1-2) arrange gtable[layout]
## 3 3 (4-5,3-4) arrange gtable[layout]
## 4 4 (6-7,1-2) arrange gtable[layout]
## 5 5 (6-7,3-4) arrange gtable[layout]
## 6 6 (3-3,4-4) arrange gtable[guide-box]
## 7 7 (1-1,1-4) arrange text[GRID.text.8385]
## TableGrob (7 x 4) "arrange": 7 grobs
## z cells name grob
## 1 1 (2-3,2-3) arrange gtable[layout]
## 2 2 (4-5,1-2) arrange gtable[layout]
## 3 3 (4-5,3-4) arrange gtable[layout]
## 4 4 (6-7,1-2) arrange gtable[layout]
## 5 5 (6-7,3-4) arrange gtable[layout]
## 6 6 (3-3,4-4) arrange gtable[guide-box]
## 7 7 (1-1,1-4) arrange text[GRID.text.8704]
## TableGrob (7 x 4) "arrange": 7 grobs
## z cells name grob
## 1 1 (2-3,2-3) arrange gtable[layout]
## 2 2 (4-5,1-2) arrange gtable[layout]
## 3 3 (4-5,3-4) arrange gtable[layout]
## 4 4 (6-7,1-2) arrange gtable[layout]
## 5 5 (6-7,3-4) arrange gtable[layout]
## 6 6 (3-3,4-4) arrange gtable[guide-box]
## 7 7 (1-1,1-4) arrange text[GRID.text.9023]
## TableGrob (7 x 4) "arrange": 7 grobs
## z cells name grob
## 1 1 (2-3,2-3) arrange gtable[layout]
## 2 2 (4-5,1-2) arrange gtable[layout]
## 3 3 (4-5,3-4) arrange gtable[layout]
## 4 4 (6-7,1-2) arrange gtable[layout]
## 5 5 (6-7,3-4) arrange gtable[layout]
## 6 6 (3-3,4-4) arrange gtable[guide-box]
## 7 7 (1-1,1-4) arrange text[GRID.text.9342]